I would check into restoring the wood floors and see how much that is. I'm afraid dying (don't know but wonder if it might seep through and totally ruin the wood floors. There is another
possibility I think that builders do at times. I think that they often buy the really cheap carpet that only lasts a year or two but it looks good because it is brand new. You can call on that
and see what it would cost to do something like this. I'm thinking if there are stains and you dye it the stains might show through that too, depending on the color you go for.
I hope this helps.
Take care,
K.